Finite Group Databasebeta

← #6715878

Subgroups — #6715878

Order 512.

1575 conjugacy classes of subgroups.

The subgroup lattice has 1283 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42957C211yesmaximal, characteristic, complemented
2#35693C211yesmaximal, characteristic
3#32963C211yesmaximal, characteristic, complemented
4#32360C211yesmaximal, characteristic, complemented
5#32348C211yesmaximal, characteristic, complemented
6#32024C211yesmaximal, characteristic, complemented
7#32001C211yesmaximal, characteristic, complemented
8#31625C211yesmaximal, characteristic, complemented
9#31613C211yesmaximal, characteristic, complemented
10#31100C211yesmaximal, characteristic, complemented
11#31078C211yesmaximal, characteristic, complemented
12#30300C211yesmaximal, characteristic, complemented
13#29975C211yesmaximal, characteristic, complemented
14#28111C211yesmaximal, characteristic, complemented
15#28101C211yesmaximal, characteristic, complemented
16#27388C211yesmaximal, characteristic, complemented
17#27370C211yesmaximal, characteristic, complemented
18#27114C211yesmaximal, characteristic, complemented
19#27099C211yesmaximal, characteristic, complemented
20#26358C211yesmaximal, characteristic, complemented
21#26342C211yesmaximal, characteristic, complemented
22#24939C211yesmaximal, characteristic, complemented
23#24933C211yesmaximal, characteristic, complemented
24#24874C211yesmaximal, characteristic, complemented
25#24866C211yesmaximal, characteristic, complemented
26#24100C211yesmaximal, characteristic, complemented
27#24088C211yesmaximal, characteristic, complemented
28#22665C211yesmaximal, characteristic, complemented
29#22661C211yesmaximal, characteristic, complemented
30#22175C211yesmaximal, characteristic, complemented
31#20878C211yesmaximal, characteristic, complemented
32C2×#547C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#480C2211yescharacteristic
36C2×#477C2211yescharacteristic
37C2×#474C2211yescharacteristic
38C2×#436C2211yescharacteristic
39C2×#435C2211yescharacteristic
40C2×#428C2211yescharacteristic
41C2×#428C2211yescharacteristic
42C22×#107C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#416C2211yescharacteristic
45#2836—21no—
46#2738—21no—
47#2737—21no—
48#2706—21no—
49#2687—21no—
50#2666—21no—
51#2663—21no—
52#2638—21no—
53#2628C2211yescharacteristic
54#2628C2211yescharacteristic
55#2583—21no—
56#2573—21no—
57#2567C2211yescharacteristic
58#2536C2211yescharacteristic
59#2508C2211yescharacteristic
60#2507C2211yescharacteristic
61#2495C2211yescharacteristic
62#2495C2211yescharacteristic
63#2487C2211yescharacteristic
64#2486C2211yescharacteristic
65#2486C2211yescharacteristic
66#2485C2211yescharacteristic
67#2470—21no—
68#2470—21no—
69#2455—21no—
70#2455—21no—
71#2440C2211yescharacteristic
72#2439C2211yescharacteristic
73#2422C2211yescharacteristic
74#2422C2211yescharacteristic
75#2407C2211yescharacteristic
76#2407C2211yescharacteristic
77#2406—21no—
78#2392C2211yescharacteristic
79#2388—21no—
80#2360C2211yescharacteristic
81#2360C2211yescharacteristic
82#2357C2211yescharacteristic
83#2354C2211yescharacteristic
84#2352C2211yescharacteristic
85D4×C4⋊C4C2211yescharacteristic
86D4×C4⋊C4C2211yescharacteristic
87#2316C2211yescharacteristic
88#2101C2211yescharacteristic
89#2101C2211yescharacteristic
90#2100C2211yescharacteristic
91#2099C2211yescharacteristic
92#2097C2211yescharacteristic
93#2095C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2087C2211yescharacteristic
97#2086C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2083C2211yescharacteristic
103#2083C2211yescharacteristic
104#2076C2211yescharacteristic
105#2076C2211yescharacteristic
106#2075C2211yescharacteristic
107#2075C2211yescharacteristic
108#2073C2211yescharacteristic
109#2071C2211yescharacteristic
110#2068C2211yescharacteristic
111#2068C2211yescharacteristic
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic
114#2058C2211yescharacteristic
115#2057C2211yescharacteristic
116#2057C2211yescharacteristic
117#2057C2211yescharacteristic
118#2057C2211yescharacteristic
119#2057C2211yescharacteristic
120#2036C2211yescharacteristic
121#2036C2211yescharacteristic
122#2035C2211yescharacteristic
123#2035C2211yescharacteristic
124#2034C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#1949C2211yescharacteristic
129#1948C2211yescharacteristic
130#1947C2211yescharacteristic
131#1947C2211yescharacteristic
132#1936C2211yescharacteristic
133#1935C2211yescharacteristic
134#1934C2211yescharacteristic
135#1933C2211yescharacteristic
136#1928C2211yescharacteristic
137#1927C2211yescharacteristic
138#1925C2211yescharacteristic
139#1925C2211yescharacteristic
140#1924C2211yescharacteristic
141#1923C2211yescharacteristic
142#1921C2211yescharacteristic
143#1921C2211yescharacteristic
144#1918C2211yescharacteristic
145#1918C2211yescharacteristic
146#1917C2211yescharacteristic
147#1916C2211yescharacteristic
148#1895C2211yescharacteristic
149#1894C2211yescharacteristic
150#1893C2211yescharacteristic
151#1892C2211yescharacteristic
152#1873C2211yescharacteristic
153#1872C2211yescharacteristic
154#1870C2211yescharacteristic
155#1869C2211yescharacteristic
156#1869C2211yescharacteristic
157#1869C2211yescharacteristic
158#1865C2211yescharacteristic
159#1865C2211yescharacteristic
160#1864C2211yescharacteristic
161#1864C2211yescharacteristic
162#1863C2211yescharacteristic
163#1863C2211yescharacteristic
164#1863C2211yescharacteristic
165#1863C2211yescharacteristic
166#1862C2211yescharacteristic
167#1862C2211yescharacteristic
168#1862C2211yescharacteristic
169#1862C2211yescharacteristic
170#1854C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1853C2211yescharacteristic
174#1852C2211yescharacteristic
175#1852C2211yescharacteristic
176#1852C2211yescharacteristic
177#1852C2211yescharacteristic
178#1852C2211yescharacteristic
179#1852C2211yescharacteristic
180#1851C2211yescharacteristic
181#1850C2211yescharacteristic
182#1847C2211yescharacteristic
183#1845C2211yescharacteristic
184#1824C2211yescharacteristic
185#1824C2211yescharacteristic
186#1823C2211yescharacteristic
187#1823C2211yescharacteristic
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1808C2211yescharacteristic
192#1808C2211yescharacteristic
193#1807C2211yescharacteristic
194#1805C2211yescharacteristic
195#1804C2211yescharacteristic
196#1798C2211yescharacteristic
197#1788C2211yescharacteristic
198#1788C2211yescharacteristic
199#1776C2211yescharacteristic
200C4×#106C2211yescharacteristic
201C2×#340C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41—21no—
204C22×#41C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#547—42no—
210#547—42no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#123—21no—
214C2×#123—21no—
215C2×#123—21no—
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225#520—42no—
226#520—42no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×D4—21no—
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117—21no—
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C22×C4⋊C4—21no—
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248#482—42no—
249#480—42no—
250#477—42no—
251#474—42no—
252#436—24no—
253#435—24no—
254#428—42no—
255#428—42no—
256C2×#107—42no—
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281#417—24no—
282#416—42no—
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#399—21no—
316#399—21no—
317#399—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398D411yescharacteristic
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397D411yescharacteristic
334#396—21no—
335#396D411yescharacteristic
336#396D411yescharacteristic
337#395—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#395—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394D411yescharacteristic
349#394D411yescharacteristic
350#394D411yescharacteristic
351#393—21no—
352#393—21no—
353#393—21no—
354#392—21no—
355#392—21no—
356#392D411yescharacteristic
357#391—21no—
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#390—21no—
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#383—21no—
421#383—21no—
422#382—21no—
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#381—21no—
427#381—21no—
428#381—21no—
429#380—21no—
430#380—21no—
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—44no—
500C2×#41—82no—
501C2×#41—82no—
502C22×Q8—21no—
503C22×Q8—21no—
504C22×Q8C2411yescharacteristic
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4C2×D411yescharacteristic
509C22×D4C2×D411yescharacteristic
510C22×D4C2×D411yescharacteristic
511C22×D4C2411yescharacteristic
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C2×M16—22no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16—41no—
528C2×M16#4114yescomplemented
529C22×C8—22no—
530C22×C8—22no—
531C22×C8—41no—
532C22×C8—41no—
533C22×C8—41no—
534C22×C8—41no—
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C4⋊Q8—41no—
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547#123—44no—
548#123—44no—
549#123—82no—
550#123—82no—
551#123—82no—
552#123—82no—
553C22⋊Q8—22no—
554C22⋊Q8—22no—
555C22⋊Q8—41no—
556C22⋊Q8—41no—
557C22⋊Q8—44no—
558C22⋊Q8—82no—
559#121—22no—
560#121—22no—
561#121—41no—
562#121—41no—
563C4×Q8—22no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—44no—
578C4×D4—44no—
579C4×D4—82no—
580C4×D4—82no—
581#117—41no—
582#117—41no—
583#117—44no—
584#117—41no—
585#117—41no—
586#117—41no—
587#117—41no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—44no—
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697#107—22no—
698#107—22no—
699#107—22no—
700#107—41no—
701#107—41no—
702#107—41no—
703#107—41no—
704#107—41no—
705#107—41no—
706#107—41no—
707#107—41no—
708#107—41no—
709#107—41no—
710#107—41no—
711#106—22no—
712#106—41no—
713#106—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717C4⋊C8—22no—
718C4⋊C8—22no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721#103—22no—
722#103—22no—
723#103—22no—
724#103—22no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—41no—
736#102—41no—
737C22⋊C8—22no—
738C22⋊C8—22no—
739C22⋊C8—22no—
740C22⋊C8—22no—
741C22⋊C8—41no—
742C22⋊C8—41no—
743C22⋊C8—41no—
744C22⋊C8—41no—
745#97—22no—
746C4×C8—22no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791C24—21no—
792C24C22×D411yescharacteristic
793C24C22×D411yescharacteristic
794C24C22×D411yescharacteristic
795#41—28no—
796#41—44no—
797#41—44no—
798#41—44no—
799#41—816no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—42no—
806C2×Q8—81no—
807C2×Q8—81no—
808C2×Q8—81no—
809C2×Q8—81no—
810C2×Q8—81no—
811C2×Q82−1+412yes—
812C2×D4—22no—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—22no—
816C2×D4—22no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—41no—
823C2×D4—41no—
824C2×D4—41no—
825C2×D4—41no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4H(5,𝔽2)12yes—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—24no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C2×#4112yes—
903C22×C42−1+412yes—
904C22×C4C2511yescharacteristic
905M16—44no—
906M16—44no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—44no—
930C2×C8—82no—
931C2×C8C2×#4112yes—
932C2×C8C2×#4112yes—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4H(5,𝔽2)12yes—
997C22⋊C4—24no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—42no—
1042C42—42no—
1043C42—42no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—22no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23#54712yes—
1076C23#57612yes—
1077C23C23×D411yescharacteristic
1078Q8—22no—
1079Q8—22no—
1080Q8—41no—
1081Q8—41no—
1082Q8—84no—
1083Q8—162no—
1084D4—22no—
1085D4—22no—
1086D4—44no—
1087D4—44no—
1088D4—44no—
1089D4—48no—
1090D4—41no—
1091D4—41no—
1092D4—84no—
1093D4—84no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—22no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—48no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—84no—
1184C2×C4—84no—
1185C2×C4—84no—
1186C2×C4—162no—
1187C2×C4—162no—
1188C2×C4—162no—
1189C2×C4—162no—
1190C2×C4#54712yes—
1191C2×C4#57812yes—
1192C2×C4C22×#4111yescharacteristic
1193C2×C4C2×H(5,𝔽2)11yescharacteristic
1194C2×C4C2×H(5,𝔽2)11yescharacteristic
1195C2×C4C2×2−1+411yescharacteristic
1196C2×C4C2×2−1+411yescharacteristic
1197C2×C4#58511yescharacteristic
1198C8—22no—
1199C8—22no—
1200C8—41no—
1201C8—41no—
1202C8—41no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C22—22no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—22no—
1211C22—22no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—42no—
1224C22—41no—
1225C22—41no—
1226C22—42no—
1227C22—41no—
1228C22—42no—
1229C22—41no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22C2×#54711yescharacteristic
1235C22#348411yescharacteristic
1236C22#348911yescharacteristic
1237C22C2×#57611yescharacteristic
1238C22C2×#57811yescharacteristic
1239C22#358511yescharacteristic
1240C22#358611yescharacteristic
1241C4—22no—
1242C4—22no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—42no—
1249C4—41no—
1250C4—41no—
1251C4—42no—
1252C4—41no—
1253C4—41no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4#345911yescharacteristic
1268C4#349211yescharacteristic
1269C4#353511yescharacteristic
1270C4#353811yescharacteristic
1271C2—42no—
1272C2—42no—
1273C2—81no—
1274C2—82no—
1275C2#3776011yescharacteristic
1276C2#6127011yescharacteristic
1277C2#6127311yescharacteristic
1278C2#6160911yescharacteristic
1279C2#6169311yescharacteristic
1280C2#6220611yescharacteristic
1281C2#6222611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35693C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #42957C2semidirect
3. #32963C2semidirect
4. #32360C2semidirect
5. #32348C2semidirect
6. #32024C2semidirect
7. #32001C2semidirect
8. #31625C2semidirect
9. #31613C2semidirect
10. #31100C2semidirect
11. #31078C2semidirect
12. #30300C2semidirect
13. #29975C2semidirect
14. #28111C2semidirect
15. #28101C2semidirect
16. #27388C2semidirect
17. #27370C2semidirect
18. #27114C2semidirect
19. #27099C2semidirect
20. #26358C2semidirect
21. #26342C2semidirect
22. #24939C2semidirect
23. #24933C2semidirect
24. #24874C2semidirect
25. #24866C2semidirect
26. #24100C2semidirect
27. #24088C2semidirect
28. #22665C2semidirect
29. #22661C2semidirect
30. #22175C2semidirect
31. #20878C2semidirect
528. C2×M16#41semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#429572
#356932
#329632
#323602
#323482
#320242
#320012
#316252
#316132
#311002
#310782
#303002
#299752
#281112
#281012
#273882
#273702
#271142
#270992
#263582
#263422
#249392
#249332
#248742
#248662
#241002
#240882
#226652
#226612
#221752
#208782